The posts were also not filmed in a hotel, with Payne saying they had been staying at “their lovely friend Gon’s house”.
In one clip, the pair joke about how late they are having breakfast, at around 1pm local time.
Payne spoke to the camera about his polo plans: “Today, we ride. I think I’m going to be playing polo again, which is going to put me out of action for about six weeks.
“Honestly, polo, out of everything I’ve ever done sports-wise, not that I’m taking up polo professionally, by the way, I’m just like, I had a go for some fun.
“It’s so hard to do, number one. Number two, my back and my neck from swinging that hammer around, or mallet, I think it’s called, if you’re in the know, it’s polo language.”
He added: “It’s a lovely day here in Argentina.”
Payne showed the views from his friend’s house overlooking fields and trees.
The posts also included images of the couple posing together and a video of Payne walking around saying: “I look like the Joker, my hair’s a bit cray-cray.”
One post also featured Cassidy and their dog watching TV, with Payne asking fans to write a caption for him.
In a statement, police said they discovered Payne’s body after an emergency crew responded to an call in the upscale neighbourhood of Palermo on Wednesday.
Payne had risen to global fame as part of the much-loved boyband created on the X Factor TV show in 2010, along with Harry Styles, Louis Tomlinson, Niall Horan and Zayn Malik.
Tributes have been flooding in from stars including Olly Murs and Dermot O’Leary.
The BBC has seen a cease and desist letter against the singer earlier this week from another of Payne’s former partners, Maya Henry, which “pertains to alleged egregious conduct”.